A rectangular pool is 6 meters wide and 14 meters long. If you swim diagonally from one corner to the other, how many meters will you swim? Approximate the answer to the nearest tenth.
a) 2.8 meters
b) 15.2 meters
c) 4.3 meters
d) 12.6 meters
We can use the Pythagorean theorem to solve this problem. The diagonal of the rectangle is the hypotenuse of a right triangle where the width and length of the pool are the other two sides.
Using the Pythagorean theorem, we have:
Diagonal^2 = Width^2 + Length^2
Diagonal^2 = 6^2 + 14^2
Diagonal^2 = 36 + 196
Diagonal^2 = 232
Taking the square root of both sides, we find:
Diagonal = √232 ≈ 15.2 meters
Therefore, the answer is (b) 15.2 meters.
A 26-foot ladder is leaning against the side of a house so that the bottom of the ladder is 10 feet from the base of the house. Will the ladder reach a window that is 22.5 feet above the ground?
a) No, because the ladder will only reach 24 feet high
b) No, because the ladder will only reach 13 feet high
c) Yes, because the ladder will reach 24 feet high
d) Yes, because the ladder will reach 32 feet high
We can use the Pythagorean theorem to solve this problem. The ladder, the side of the house, and the ground form a right triangle.
Using the Pythagorean theorem, we have:
Ladder^2 = Height^2 + Distance^2
26^2 = 22.5^2 + 10^2
676 = 506.25 + 100
676 = 606.25 + 100
676 = 706.25
Since 676 is less than 706.25, the ladder will not reach the window that is 22.5 feet above the ground.
Therefore, the answer is (b) No, because the ladder will only reach 13 feet high.